A338299 Primes of the form (p^2+p+1)/3 where p is prime.

19, 61, 127, 331, 631, 1801, 3169, 3571, 5419, 8269, 13267, 16651, 19441, 24571, 55897, 59221, 145861, 151201, 176419, 246247, 260191, 292969, 347821, 360187, 368551, 377011, 398581, 698419, 733591, 863497, 915769, 929077, 990151, 1024921, 1155061, 1177507, 1324681, 1372957, 1618471, 1980469

Offset: 1

Author

J. M. Bergot and Robert Israel, Oct 21 2020

Keywords

• nonn

Comments

All terms == 1 (mod 6).

Examples

			a(3) = 127 is prime and 127 = (19^2+19+1)/3 where 19 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A240971.

Programs

Maple

A240971:= select(t -> isprime(t) and isprime((t^2+t+1)/3), [seq(i,i=1..1000,6)]):
map(t -> (t^2+t+1)/3, A240971);

Formula

a(n) = (A240971(n)^2 + A240971(n)+1)/3.

A240971(n) = (sqrt(12*a(n)-3)-1)/2.